Long time existence of a class of contact discontinuities for second order hyperbolic balance laws

Abstract

The study of long time existence of classical smooth solutions for second order quasilinear wave equations has received much attention (see e.g. [1] and the references given there). Results were also obtained for continuous semilinear waves with gradient jumps on a characteristic hypersurface in [2] and for C1 quasilinear waveswith second order derivatives jumps on a characteristic hypersurface in [3], [4]. In this paper we show how the methods and results of [2] can be extended to a class of continuous weak solutions, with gradient jumps on a characteristic hypersurface, for some second order quasilinear balance laws.

Keywords

• second order quasilinear wave equations
• semilinear waves with gradient jumps on a characteristic hypersurface.